Hechavarria collected a one-out single in the 10th against Brian Duensing (4-12) and went to second on a wild pitch.
After J.P. Arencibia struck out, Gose sent a grounder up the middle for the decisive tally.
Brandon Lyon (4-0) earned the win as the Blue Jays took the opener of a season-ending three-game series.
Trevor Plouffe drove in three runs and Jamey Carroll went 3-for-5 with an RBI for Minnesota.
Police: Sword-wielding man demanded free tacos
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph